ODE45, differential equation

my function is

dy/dt=k*y*exp(450/y)

k is constant and y(0)=40 and y(15)=95 solve this equation by using ode45 can someone pleaseeeeeeeeeee check the code and make it work .

tspan = [0 300];
y0 = 40;y15=95
[t,y] = ode45(@(t,y) 'k'*y*exp(450/y), tspan, y0,y15);
plot(t,y,'-o')

Answer 1

[Stephan]

Hi,

if you search a value for k that complies with the boundary conditions, you could use fzero to solve the problem numerically:

k = fzero(@calculate_k, 0.001);
disp(['k = ', num2str(k)])
[t,y] = ode45(@(t,y) k*y*exp(450/y), [0 300], 40);
plot(t,y,'r')
hold on
scatter(15,95,'ob')
text(23,96,'y(t=15) = 95','Color','b')
hold off

function k_value = calculate_k(x)
tspan = [0 15];
y0 = 40;
[~,y] = ode45(@(t,y) x*y*exp(450/y), tspan, y0);
k_value = y(end) - 95;
end

This will give you as result:

k = 0.00010435

or if you need it more accurate:

k =

       1.043495007807761e-04

and the plot which belongs to this result looks like the boundary conditions are met (To be precise, it keeps the boundary conditions. This is because fzero is a powerful tool and also because you can think of a very good initial value for x0 with just a few estimates...):

.

Best regards

Stephan

[Takey Asaad]

Thanks so much

[Stephan]

No problem - please be patient with your questions. Dont ask the same question a second time, if it needs more time than you expected to get an answer.

Better try to give as much as and as good as possible informations that are needed to let the contributers give you a useful answer.

Answer 2

[James Tursa]

Remove the quotes from 'k', and be sure to define k before you call ode45. Also, ode45 is an initial value problem solver, so the y15 variable is not applicable (remove it from the call).

[Takey Asaad]

Hi, k is constant and MATLAB should calculate it from the 2 conditions, so can you please help.

[James Tursa]

Oh, I misunderstood. Since you are solving for k, this is not an initial value problem and ode45 is not the appropriate tool to use as I have outlined it. You might look at the boundary value problem link here:

https://www.mathworks.com/help/matlab/ref/bvp4c.html?s_tid=doc_ta

And read the discussion following:

"The bvp4c solver can also find unknown parameters p for problems of the form ..."

[Takey Asaad]

Can you please do it , i still have problem, i am new to MATLAB

[James Tursa]

You need to make an attempt at this. Look at the example involving an unknown parameter, and try to use that as an outline for your equation.

[Takey Asaad]

i did and still, so if you know can you help please?

[James Tursa]

Please post your current code and let us know what specific problems you are having with it.

[Takey Asaad]

function bvp4
xlow=0;xhigh=300;
solinit=bvpinit(linspace(xlow,xhigh,300),[40 95]);
sol=bvp4c(@bvp4ode,@bvp4bc,solinit);
xinit=linspace(xlow,xhigh,20);
sxint=deval(sol,xint);
plot(xint,sxint(1,:);
function dydx=bvp4ode(x,y)
dydx=[y(2) a*y*exp(450/y);
    function res=bvp4bc(ya,yb)
    res=[ya(1)-1,yb(1)

[Takey Asaad]

function bvp4
xlow=0;xhigh=300;
solinit=bvpinit(linspace(xlow,xhigh,300),[40 95]);
sol=bvp4c(@bvp4ode,@bvp4bc,solinit);
xinit=linspace(xlow,xhigh,20);
sxint=deval(sol,xint);
plot(xint,sxint(1,:);
function dydx=bvp4ode(x,y)
dydx=[y(2) a*y*exp(450/y);
    function res=bvp4bc(ya,yb)
    res=[ya(1)-1,yb(1)
 function bvp4
 ↑
Error: Function definition not supported in this context. Create functions in code file.

[Takey Asaad]

function bvp4
xlow=0;xhigh=300;
solinit=bvpinit(linspace(xlow,xhigh,300),[40 95]);
sol=bvp4c(@bvp4ode,@bvp4bc,solinit);
xinit=linspace(xlow,xhigh,20);
sxinit=deval(sol,xint);
plot(xinit,sxinit(1,:);
function dydx=bvp4ode(x,y)
dydx=[y(2) ,a*y*exp(450/y)];
    function res=bvp4bc(ya,yb)
    res=[ya(1)-1,yb(1)]

Answer 3

[Takey Asaad]

if true
  function bvp4
xlow=0;xhigh=300;
solinit=bvpinit(linspace(xlow,xhigh,300),[40 95]);
sol=bvp4c(@bvp4ode,@bvp4bc,solinit);
xinit=linspace(xlow,xhigh,20);
sxinit=deval(sol,xint);
plot(xinit,sxinit(1,:);
function dydx=bvp4ode(x,y)
dydx=[y(2) ,a*y*exp(450/y)];
  function res=bvp4bc(ya,yb)
  res=[ya(1)-1,yb(1)]
end

Answer 4

[Takey Asaad]

code